# Circuit Theory/Phasors/Examples/example11

Complex 2R, L, C, voltage circuit

Given that the voltage source is defined by $V_s(t) = cos(t)$ and the current source is defined by $I_s(t) = 2sin(t-\frac{\pi}{3})$, find all other voltages, currents and check power.

Circuit marked up for analysis

## Knowns, Unknowns and Equations

Knowns: $V_s, R_1, R_2, L, C, I_s$
Unknowns: $v_1, v_2, v_C, v_L, i_1, i_2, i_C, i_L$
Equations:
$v_1 = R_1 * i_1$
$v_2 = R_2 * i_2$
$i_C = C * {d \over dt}v_C$
$v_L = L * {d \over dt}i_L$
$i_1 + I_s - i_2 -i_C = 0$
$i_c - I_s - i_L = 0$
$v_1 + v_2 - V_s = 0$
$v_C + v_L - v_2 = 0$

## Solutions and Analysis

numeric solution calculated in the phasor domain
attempt at a Laplace solution
simulation at circuitlab